Ratios, Rates & Proportions Chapter Questions 1. How are ratios simplified? 2. How are equivalent ratios written? 3. How are unit rates determined? 4. How can equivalent rates help to solve problems? 5. What are the two ways proportions are solved? 6. What are examples of proportions in real life?
Ratios, Rates & Proportions Chapter Problems Writing Ratios 1. Write each ratio as a fraction in simplest form. a. 9:36 = b. 10 to 100 = c. 25:75 = d. 49 7 = e. 8 out of 11 = 2. There are 20 soccer players on the team. 8 are in 7 th grade and the rest are in 8 th grade. Write the ratios below three different ways: a. The number of 7 th graders to the number of 8 th graders. b. The number of 8 th graders to the total number of players on the team. 3. There are 32 slices of pizza. 10 are plain, 12 are pepperoni, and the rest are sausage. a. What is the ratio of plain to pepperoni? b. What is the ratio of plain to sausage? c. What is the ratio of sausage to total slices? d. What is the ratio of total slices to plain? 4. Write each ratio as a fraction in simplest form. a. 7:9 = b. 10 to 6 = c. 1,000:10,000 = d. 70 125 = e. 6 out of 50 = 5. There are 15 students in the yearbook club. 3 are in 7 th grade and the rest are in 8 th grade. Write the ratios below three different ways: a. The number of 7 th graders to the number of 8 th graders. b. The number of 8 th graders to the total number of members in the club. 6. There are 24 hotdogs. 8 are plain, 10 have ketchup on them, and the rest have mustard. a. What is the ratio of plain to mustard? b. What is the ratio of plain to ketchup? c. What is the ratio of ketchup to total hotdogs? d. What is the ratio of total hotdogs to plain? Equivalent Ratios 7. The following ratios are equivalent, true or false? 3 6 a. is equivalent to 10 12 b. 22 to 50 is equivalent to 11:25 13 23 c. is equivalent to 33 66
d. 9:6 is equivalent to 3:2 e. 3 to 5 is equivalent to 12 to 20, which is equivalent to 24 to 10 24 12 f. is equivalent to is equivalent to 4 36 18 6 8. Write an equivalent ratio. a. 7 9 = b. 15 to 39 = c. 6:4 = d. e. 4 = 5 5 = 13 f. 70 to 30 = 9. The following ratios are equivalent, true or false? 7 14 a. is equivalent to 12 24 b. 9 to 20 is equivalent to 27:40 8 16 c. is equivalent to 11 22 d. 40:8 is equivalent to 20:2 e. 4 to 7 is equivalent to 8 to 14, which is equivalent to 20 to 35 50 10 f. is equivalent to is equivalent to 5 75 15 7 10. Write an equivalent ratio. Rates a. 8 13 = b. 28 to 49 = c. 2:3 = d. e. 7 = 9 80 = 20 f. 45 to 35 = 11. At the party there was 32 slices of pizza for 16 kids. How many slices per person? 12. The new car can travel 400 miles on 20 gallons of gas. How many miles per gallon can the car travel? 13. There are 5 coaches at the field for 40 kids. How many kids per coach are there? 14. The recipe calls for 5 cups of sugar for every 2 eggs. How many cups of flour are needed for one egg? 15. 8 cups of water evaporate in 4 days. How many cups of water evaporate per day? 16. Below are some sale prices for yogurt. Which offers the best price? a. 15 for $3.95 b. 5 for $2.20
c. 20 for $6.20 d. 10 for $3.20 17. It costs $46.20 for 7 pizzas. What is the cost per pizza? 18. There are 576 calories in 8 servings of pie. What is the number of calories per slice? 19. A discount store is having a sale on CDs. Seven CDs cost $65.45, what is the price per CD? 20. You earn $60 for eight hours of work. What is the hourly rate? 21. You can type 405 words in 4.5 minutes. How many words can you type in one minute? 22. Below are some sale prices for soda. Which offers the best price? a. 6 for $1.75 b. 8 for $1.90 c. 12 for $3.15 d. 30 for $7.50 Writing an Equivalent Rate 23. Write the equivalent rates by filling in the missing information. 50 mi a. =? mi. 1 hour 1 day b. 1 month = 1 year $800?dollars 35 feet c. =?feet 5 hours 1 hours 700 people d. =?people 5 days hour 24. Write the equivalent rates by filling in the missing information. $9.50 a. =?dollars 1 hour 40 hours 50 pounds b. = 5 pounds $23.50?dollars c. 25 yards =?yards 2.5 seconds 10 seconds d.?ounces = 5 ounces $1.65 $2.75 Proportions
25. Solve the proportion using equivalent ratios. a. 2 7 = 4 x b. 5 9 = x 27 c. 20 11 = x 22 d. 36 48 = 6 x e. x 3 = 30 45 26. Use cross products to solve the proportion. a. 2 6 = 5 x b. 4 6 = x 9 c. 5 25 = x 20 d. 6 2 = 21 x e. x 18 = 6 4 27. Socks are 3 pairs for $4.25. If you want to buy 10 pairs, how much will that cost? Set up a proportion and solve. 28. T-shirts cost $8.00 for 5, how many can you get with $20? Set up a proportion and solve. 29. Solve the proportion using equivalent ratios. a. 2 3 = x 9 b. 6 10 = 3 x c. 10 x = 15 3 d. x 3 = 8 12 e. 12 = 3 x 1.2 30. Use cross products to solve the proportion. a. 4 = 3 x 9 b. 20 = 16 x 20 c. 3 = 7 6 x d. x = 25 42 70 e. 36 = 27 x 21
31. Shorts are 3 for $20.00. You want to buy 5, how much will that cost? Set up a proportion and solve. 32. Tank tops cost $7.25 for 2, how many can you get with $25? Set up a proportion and solve. Application Problems 33. Two friends take a bicycle trip. Ricky rides 10 miles in 0.75 an hour. Victoria rides 15 miles in 1.25 hour. Which bicycle rider has the slower rate? 34. Your team scores 2 runs in the first three innings of a 9-inning baseball game. If your team continues to score at that rate, how many runs will it score in the game? 35. A quality control inspector found four defective cell phones out of 480. At that rate, how many defective cell phones would there be out of 24,000? 36. Eight ounces of orange juice contain 120 calories. About how many calories are in 12 ounces of orange juice? 37. At the copy store, 15 copies cost $.75, you need 50 copies. About how much will they cost? 38. You are testing orange juice recipes. Each recipe calls for orange juice concentrate and water. Mix 1 has 4 cups of concentrate and 6 cups of water, Mix 2 has 1 cup of concentrate and 3 cups of water, and Mix 3 has 2 cups of concentrate and 4 cups of water. Which mix will be the most orangey, which will be the least orangey? 39. There are two size tables at a birthday party. One table seats 10 people and one seats 6. If the table for 10 has 3 cakes on it, and the table for 6 has 2 cakes on it, and the cake is shared equally, will a person sitting at the small table get as much cake as a person sitting at the large? 40. A car traveling 102 miles uses 3 gallons of gas. At this rate, how far can the car travel using 14 gallons of gas? 41. In three hours, you can pack 48 cartons of books. How many cartons of books can be packed in 8 hours? 42. The garden center has a sale, 5 plants for $18. How much would you spend if you bought 15 plants? 43. Your friend can run 17 miles in 2 hours. If your friend could run for 6 hours at the same rate, how many miles would be run? 44. If 3 pounds of chocolate cost $25.50, how many pounds can you buy for $42.50? 45. There are 13 grams of protein in 2 ounces of tuna. How many ounces do you need to eat to get 45.5 grams of protein?
46. The athletic boosters club is sponsoring a spaghetti dinner. Jars of spaghetti sauce are on sale for 5 for $6.25. How many jars will be needed if 120 people are expected to attend? What will be the cost? 47. Two different brands of cereal are on sale at the supermarket this week. One sale is two boxes for $3.80 and the other sale is five boxes for $9.00. Which sale is the better buy? 48. A dozen bagels cost $7.20. At this rate, how much will 7 cost? Sampling 49. In a survey of 300 voters, 68 said they voted for Candidate A. How many votes can Candidate A expect to receive if the population of the town is 10,000? 50. In a capture-recapture study, 97 grizzly bears were tagged and released back into the wild. A month later, 200 bears were captured of which 36 were tagged. About how many grizzly bears are in the population? 51. In a capture-recapture study, 83 mountain lions were tagged and released back into the wild. Several months later, 300 mountain lions were captured, of which 54 were tagged. About how many mountain lions are in the population? 52. In a survey of 1056 voters at Roberts School, 274 said they voted for Candidate A. How many votes can Candidate A expect to receive if there were 5,101 votes? Scale Drawings 53. On a map, the scale is ½ inch : 25 miles. What is the actual distance between two cities that are 3 inches apart? 54. What are the dimensions of a 15 foot by 10 foot room on a blueprint with a scale of 1.5 inches : 2 feet? 55. The distance between Newark, NJ and San Francisco, CA is 2,888 miles. How far would that measure on a map with a scale of 3 cm to 1,000 miles? 56. If the scale for a model train is 1 inch for every 10 feet of a real train, how big is the model for an 83- foot train? 57. On a map, the scale is 1.5 inches : 20 miles. If two cities are 115 miles apart, how far apart are they on the map? 58. A model of a dinosaur built to a scale of 3 cm : 1 m is 24 centimeters tall. How tall was the actual dinosaur?
59. What are the dimensions of a building whose dimensions on a blueprint are 1.8 cm by 2.4 cm? The blueprint s scale is 1 cm : 15 feet. 60. The distance between two cities is 180 miles. How far does that measure on a map with a scale of 1 inch : 25 miles? Similar Figures 61. Are the figures similar? Justify your answer. 9 cm 2 cm 3 cm 1 cm 62. Find the value of x in the pair of similar polygons. 63. Find the value of x in the pair of similar polygons. 64. Are the figures similar? Justify your answer. 3 ft 3 ft 1.5 ft 6 ft 65. Find the value of x in the pair of similar polygons. X in 2 in 0.5 in 6 in
66. Find the value of x in the pair of similar polygons. 3 cm 3 cm 6 cm 6 cm x cm 5 cm 1. 2. 3. 4. 5. 6. 7. a. ¼ b. 1/10 c. 1/3 d. 7 e. 8/11 a. 2:3 b. 3:5 a. 5:6 b. 1:1 c. 5:16 d. 16:5 a. 7/9 b. 5/3 c. 1/10 d. 14/25 e. 3/25 a. ¼, 1:4, 1 to 4 b. 4/5, 4:5, 4 to 5 a. 4:3 b. 4:5 c. 5:12 d. 3:1 Answer Key
a. False b. True c. False d. False e. False f. True 8. a. 14:18 b. 30:78 c. 12:8 d. 8:10 e. 10:26 f. 7:3 9. a. True b. False c. True d. False e. True f. False 10. a. 16/26 Multiple Answers b. 4 to 7 Multiple Answers c. 4:6 Multiple Answers d. 14/18 Multiple Answers e. 8/2 Multiple Answers f. 9 to 7 Multiple Answers 11. 2 12. 20 13. 8 14. 2.5 15. 2 16. C 17. $6.60 18. 72 19. $9.35 20. $7.50 21. 90 22. B 23. a. 1000 mi b. $800 c. 7 ft. d. 140 people 24. a. $380 b. $2.35 c. 100 yds. d. 3 oz. 25. a. 14 b. 15
c. 40 d. 8 e. 2 26. a. 15 b. 6 c. 4 d. 7 e. 27 27. $14.16 28. 12 shirts 29. a. 6 b. 5 c. 2 d. 2 e. 4.8 30. a. 12 b. 25 c. 14 d. 15 e. 28 31. $33.33 32. 6 33. Victoria 34. 6 35. 200 36. 180 37. $2.50 38. Most: Mix 1, Least: Mix 2 39. Larger 40. 476 41. 128 42. 54 43. 51 mi 44. 5 45. 7 46. 120 jars, $150 47. $9 for 5 boxes 48. 4.2 49. 2266 50. 261 51. 329 52. 1323 53. 150 54. 11.25 by 7.5 55. 8.66 cm 56. 8.3 in. 57. 8.63 in. 58. 8m 59. 27 by 36
60. 7.2 in 61. No. 9/3 2/1 62. 3.78 63. 9 64. Yes 3/1.5 = 6.4 65. 1.5 66. 2.5 cm